The five number summary for a set of data is given below. Min Q1 Median Q3 Max 80 84 86 90 99 What is the interquartile range of the set of data? Enter just the number as your answer. For example, if you found that the interquartile range was 17, you would enter 17. Provide your answer below: FEEDBACK MORE INSTRUCTION SUB Content attribution
The Correct Answer and Explanation is :
The interquartile range (IQR) is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). Using the five-number summary provided:
- Q1 = 84
- Q3 = 90
The formula for the interquartile range is:
[
IQR = Q3 – Q1
]
Substituting the values:
[
IQR = 90 – 84 = 6
]
So, the interquartile range for this dataset is 6.
Explanation:
The five-number summary gives us a good summary of the distribution of the data. It consists of:
- Minimum: The smallest data point (80).
- Q1 (First Quartile): The median of the lower half of the data (84). This represents the 25th percentile of the data.
- Median (Second Quartile): The middle value of the dataset (86).
- Q3 (Third Quartile): The median of the upper half of the data (90). This represents the 75th percentile of the data.
- Maximum: The largest data point (99).
The interquartile range is a measure of statistical dispersion, or in simpler terms, how spread out the middle 50% of the data is. It tells us the range within which the central half of the data lies, helping to minimize the effect of outliers and extreme values. The IQR is especially useful because it focuses on the central portion of the data, ignoring the extreme values at the ends (min and max).
If you’d like, I can generate a box plot showing the IQR visually. Would you like me to do that?